Shockless compression of a barotropic gas (Q1314055)

A problem concerning the shockless ``cold'' compression of one- dimensional layers (planar, cylindrical and spherical) of a barotropic gas which requires a minimum amount of external energy in order to attain the specified degree of compression is formulated and solved. The initial state of gas is assumed to be homogeneous. In the planar case, an exact solution of the problem is obtained (laws for the optimal control of the motion of the piston are constructed) using Pontryagin's maximum principle while, in the cylindrical and spherical cases, an approximate solution is obtained using the method of characteristic series. In the planar case, the magnitude of the energy gain is found compared with the traditional self-similar method of compression which had turned out to be quite appreciable and to depend on the equation of state. The results of numerical calculations are presented for the cylindrical case which was studied in greater detail.